Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Not Homework. Proving question

  1. Oct 18, 2011 #1
    1. The problem statement, all variables and given/known data

    Prove that:

    [tex](\frac{10^{n}}{10^{n}-1})^{10^n} = e [/tex]

    as n approaches inf.

    2. Relevant equations

    It is rather obvious that i can let 10^{n} be yet another variable

    3. The attempt at a solution

    I proved by assuming binomial dist as Poisson dist (it is interesting for me to use this to prove a continued fraction)
  2. jcsd
  3. Oct 18, 2011 #2


    Staff: Mentor

    You can simplify by letting u = 10n and working with this limit:

    [tex]\lim_{u \to \infty}\left( \frac{u}{u - 1} \right)^u[/tex]

    The usual approach is to let y = (u/(u - 1))u, and then take the natural log of both sides.

    ln y = u ln(u/(u - 1)) = [ln(u/(u - 1))]/(1/u)

    Now take the limit of both sides. Note that the expression above is the limit of the log of what you want.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook